Interrupted Time-Series Design

The interrupted time-series design provides an estimate of the causal effect of a discrete intervention. In its simplest form, the design begins from a long series of repeated measurements on a DEPENDENT VARIABLE. The INTERVENTION breaks this TIME SERIES into preintervention and postintervention segments, and a data analysis compares the means of the dependent variable in the two periods. Rejecting the NULL HYPOTHESIS of no difference between the means is taken as evidence that the intervention influenced the series.

Figure1 illustrates an unusually clear example of the design's logic. The data come from a 1978 study by A. John McSweeny and consist of 180 months of local directory assistance calls in Cincinnati, Ohio. During March 1974, the Cincinnati telephone company began to charge a small fee for answering these calls, which it had previously handled for free. Call volume plummeted, supporting the idea that the fee successfully reduced demands on the service.

In this example, the causal impact of the intervention seems obvious. The number of calls fell immediately and dramatically, and no ready explanation exists for why the drop might otherwise have occurred. More typically, any change in a series will be visually ambiguous, and alternative explanations will be easier to construct. Therefore, applications of the timeseries design must address statistical analysis issues, and researchers must entertain rival explanations for an apparent causal effect.

Much of the design's popularity stems from the work of Donald T. Campbell, in collaborations with Julian C. Stanley and Thomas D. Cook. Campbell and his coworkers developed a list of threats to the INTERNAL VALIDITY of causal inferences, where variables besides the one under study might account for the results. Using their list to evaluate common nonexperimental designs, Campbell and coworkers concluded that the interrupted time series had stronger internal validity than did most alternatives.

Its relative strengths notwithstanding, the timeseries design is still vulnerable to several important validity threats. One of these is history, or the possibility that other events around the time of the intervention were responsible for an observed effect. To make historical threats less plausible, researchers often analyze control series that were not subject to the intervention.

Figure 1 Average Daily Calls (in Thousands) to Cincinnati Local Directory Assistance, January 1962–December 1976

McSweeny (1978).

Lack of change in these series increases confidence that the intervention was the causal agent. In Cincinnati, for example, the telephone company continued to provide free long-distance directory assistance, and this series did not drop after the local assistance fee began.

Statistical analyses of interrupted time-series data often rely on BOX-JENKINS MODELING. Although not absolutely required, Box-Jenkins methods help solve two major analytic problems: nonstationarity and SERIAL CORRELATION. Nonstationarity occurs when a series lacks a constant mean (e.g., when it trends), and serial correlation occurs when later observations are predictable from earlier ones. If not addressed, these features can invalidate tests of the difference between the preintervention and postintervention means.